Seismic Signal Analysis Based on Adaptive Variational Mode Decomposition for High-speed Rail Seismic Waves

To accurately evaluate the remaining life (RUL) of rolling bearings under small sample conditions and strong noise interference, a RUL prediction scheme using adaptive variational mode decomposition (VMD) and double-discriminator conditional CycleGAN (DD-cCycleGAN) is put forward. Combining chimp optimization algorithm (ChOA) with VMD, an adaptive VMD algorithm based on ChOA is presented, which selects effective mode components for reconstruction and reduces interference from strong background noise. A DD-cCycleGAN is developed to generate new samples which not only retain sample information of source domain, but also resemble samples of target one. A LSTM network after training is utilized to predict the bearing RUL in test samples. The performance of this scheme was validated by using the XJTU-SY bearing test dataset. The comparison analyses demonstrate this scheme has strong noise resistance and high accuracy.

Variational mode decomposition has been widely applied to machinery fault diagnosis during these years. However, it remains difficult to set proper hyperparameters for the variational mode decomposition, including number of decomposed modes, initial center frequencies, and balance parameter. Moreover, the low efficiency of the existing variational mode decomposition methods hinders their applications to practical diagnostic task. This article proposes an adaptive and efficient variational mode decomposition method after thoroughly investigating its convergence property characteristic. A convergent tendency phenomenon is discovered and is explained mathematically for the first time. Motivated by the convergent tendency phenomenon, the proposed method rapidly and adaptively determines the number and the optimal initial center frequencies of signal latent modes with the guidance of the convergent tendencies of the initial center frequencies changing from small to large. In the proposed method, the number of decomposed modes and initial center frequencies are not hyperparameters that require to be set in advance any more, but are parameters learned from the analyzed signals. The determined parameters enable efficient extraction of the main latent modes contained in the analyzed signals. Therefore, the proposed variational mode decomposition method represents a major improvement in parameter adaption and decomposition efficiency over the existing variational mode decomposition methods. In the application for bearing fault diagnosis, the faulty modes are selected adaptively and the corresponding balance parameters are further optimized efficiently. Two experimental cases validate the proposed method and its superiority over the existing variational mode decomposition methods and the classical fast spectral kurtosis in bearing fault diagnosis.

To accurately extract fault information from rolling bearing (RB) vibration signals with strong nonlinear and non-stationary characteristics, a novel method using adaptive variational mode decomposition with noise suppression and fast spectral correlation (AVMDNS-FSC) is proposed. The AVMDNS algorithm can adaptively select VMD parameters K and α, which reduces the error caused by the improper selection of VMD parameters based on experience or prior knowledge of the signal. Meanwhile, the AVMDNS also effectively suppresses noise in intrinsic mode function (IMFs) and avoids unexpected removal of the IMFs containing important fault information. In addition, the FSC can further suppress residual noise and interference harmonics to enhance the periodic fault pulses and hence accurately extract bearing fault features. Simulation analysis and experimental studies are carried out through comparison with other methods. Results show that the AVMDNS-FSC method has higher sensitivity and effectiveness in extracting early periodic fault pulses of RB vibration signals.

Proton exchange membrane fuel cell (PEMFC) degradation prediction is essential, especially in the industrial power generation system, since it can provide decision supports for equipment maintenance. As degradation phenomena inside PEMFC are strongly nonlinear and inter-coupled, accurate degradation prediction is extremely challenging. Thus, a novel data-driven prediction method based on the adaptive variational mode decomposition (AVMD) and deep belief network (DBN) is proposed. Firstly, an improved AVMD method is employed to decomposes the original voltage series into multiple sub-signals, which helps to analyze the different degradation characteristics of PEMFC. Then, the sample entropy (SE) theory is employed to filter out the noise sub-signals and reconstruct the rest sub-signals to strengthen significant features. Finally, the predictions are performed for each reconstructed sub-signal by the DBN method that has powerful mining ability for latent degradation features. The overall prediction results of the AVMD-DBN method are in good agreement with real experimental data, which indicates that the proposed method has good practicality for the health management of the PEMFC power generation system in industrial applications.

A motor bearing system is a nonlinear dynamics system with nonlinear support stiffness. It is an asymmetry system, which plays an extremely important role in rotating machinery. In this paper, a center frequency method of double thresholds is proposed to improve the variational mode decomposition (VMD) method, then an adaptive VMD (called DTCFVMD) method is obtained to extract the fault feature. In the DTCFVMD method, a center frequency method of double thresholds is a symmetry method, which is used to determine the decomposed mode number of VMD according to the power spectrum of the signal. The proposed DTCFVMD method is used to decompose the nonlinear and non-stationary vibration signals of motor bearing in order to obtain a series of intrinsic mode functions (IMFs) under different scales. Then, the Hilbert transform is used to analyze the envelope of each mode component and calculate the power spectrum of each mode component. Finally, the power spectrum is used to extract the fault feature frequency for determining the fault type of the motor bearing. To test and verify the effectiveness of the DTCFVMD method, the actual fault vibration signal of the motor bearing is selected in here. The experimental results show that the center frequency method of double thresholds can effectively determine the mode number of the VMD method, and the proposed DTCFVMD method can accurately extract the clear time frequency characteristics of each mode component, and obtain the fault characteristics of characteristics; frequency, rotating frequency, and frequency doubling and so on.

This paper proposes a study on gearbox fault feature extraction of wind turbine under variable speed condition using improved adaptive variational mode decomposition (VMD). Frequent changes in wind speed and critical noise interference make the vibration signal exhibit non-stationary characteristics. Although computational order tracking can transform non-stationary signals in the time domain into stationary angular signals, and then extract fault features from order spectrum obtained by FFT, the obtained order spectrum is liable to be polluted by noise or to appear order aliasing. To avoid order aliasing and eliminate noise interference, the original non-stationary signal is firstly processed using the improved adaptive VMD method called adaptive differential evolution – VMD (ADE-VMD). ADE-VMD can not only utilise the advantages of traditional VMD but also adaptively select narrow-band intrinsic mode function (NBIMF) to construct the reconstructed signal with less noise and without order aliasing. In the experiment, we compared the ADE-VMD method with other VMD methods such as GA-VMD, PSO-VMD and DE-VMD, and the results showed that ADE-VMD has excellent adaptive processing ability, and its convergence and optimisation speed are more remarkable. ADE-VMD can effectively filter the noise inference and avoid the order aliasing, so it is well suitable for fault feature extraction under variable speed.

This paper proposes a medical image denoising method based on two-dimensional adaptive compact variational mode decomposition (2D-ACVMD). First, a binary support function is introduced into 2D-VMD in order to enhance its spatial compactness. The optimal decomposition mode number K and the penalty factor α can be determined by the moving average power spectrum method and the genetic algorithm, respectively. Then, the decomposed high-frequency noise component is removed, and the other modes are reconstructed to obtain the denoised image. According to the experimental results, this method can effectively remove the noise interference, retain the original edge and detail features, and the PSNR and SSIM obtained are higher than the previous methods.

Accurate wind speed prediction is a premise that guarantees the reliable operation of the power grid. This study presents a combined prediction model that integrates data preprocessing, cascade optimization, and deep learning prediction to improve prediction performance. In data preprocessing, the wavelet soft threshold denoising (WSTD) is employed to filter the blurring noise of the original data. Then, the robust empirical mode decomposition (REMD) and adaptive variational mode decomposition (AVMD) are adopted to carry out a two-stage adaptive decomposition. Spearman correlation is used to quantify the mode that need to be decomposed for the second time. In the cascade optimization, the hybrid grey wolf algorithm (HGWO) is employed to optimize the parameters of the VMD and the gated recurrent unit (GRU), which overcomes the problem of empirical parameter adjustment. The HGWO is also adopted in the prediction strategy to optimize the GRU model to predict the grouped intrinsic mode functions (IMFs). Lastly, the final wind speed prediction result is obtained by superimposing the values of all the predicted models. The proposed model was validated with the measured wind speed data of the four quarters in the Bay area of China and was compared with 20 models of the classic method to further evaluate the effectiveness of the model. The results show that the whole process of the proposed model is adaptive, the final multi-step prediction performance is good, and high prediction accuracy can be attained.

Due to the application of power electronics and wind power generation equipment in power systems, broadband oscillation events constantly appear, which makes broadband oscillation difficult to detect due to the limitations of communication bandwidth and the sampling theorem. To ensure the safety and stability of the system, and to detect and recognize the broadband oscillation information timely and accurately, this paper presents a multi-mode recognition method of broadband oscillation based on compressed sensing (CS) and the adaptive Variational Mode Decomposition (VMD) algorithm. Firstly, the high-dimensional oscillation signal data collected by the Phasor Measurement Unit (PMU) is compressed and sampled by a Gaussian random matrix, and the obtained low-dimensional data are uploaded to the main station. Secondly, the orthogonal matching pursuit (OMP) algorithm of the master station is used to reconstruct the low-dimension signal, and the original high-dimension signal data are recovered without losing the main features of the signal. Finally, an adaptive VMD algorithm with energy loss minimization as a threshold is used to decompose the reconstructed signal, and the Intrinsic Mode Function (IMF) components with broadband oscillation information are obtained. By constructing oscillating signals with different frequencies, Gaussian white noise with a signal-to-noise ratio of 10 dB to 30 dB is added successively. After the signal is compressed and reconstructed by the proposed method, the signal-to-noise ratio can reach 18.8221 dB to 40.0794 dB, etc., and the oscillation frequency and amplitude under each signal-to-noise ratio can be accurately identified. The results show that the proposed method not only has good robustness to noise, but also has good denoising effect to noise. By using the simulation measurement model, the original oscillation signal is compressed and reconstructed, and the reconstruction error is 0.1263. The basic characteristics of the signal are restored, and the frequency and amplitude of the oscillation mode are accurately identified, which proves that the method is feasible and accurate.

The bearing fault diagnosis is of vital significance in maintaining the safety of rotation machine. Among various fault detection techniques, the diagnosis based on vibration signal is widely applied in monitoring the condition of rotation machine. Variational mode decomposition (VMD) is a novel signal analysis method, which can decompose a multi-component signal into a certain number of band-limited intrinsic mode functions (BLIMFs) nonrecursively. VMD could overcome some problems such as mode mixing, the inference of noise, the determination of wavelet base, which exist in empirical mode decomposition, ensemble empirical mode decomposition, wavelet transform, respectively. However, the empirical selection of the parameters for VMD would affect the result of the decomposition. This paper presents an adaptive VMD method with parameter optimization for detecting the localized faults of rolling bearing. Kurtosis, sensitive to transient impulsive components, is employed as optimization index to evaluate the performance of the VMD. Two parameters in the VMD, namely the number of decomposition modes and data-fidelity constraint, are optimized synchronously based on the kurtosis index through artificial fish swarm algorithm. Executing VMD with the acquired parameters, the optimal BLIMF is obtained. The spectrum analysis of the optimal BLIMF could identify the characteristic frequency caused by the localized crack effectually. The validity of the proposed method is proved by means of a cyclic transient impulse response signal and two experiments with practical vibration signals of rolling bearings. Compared to several existing methods, the proposed method demonstrates reinforced results.

In the context of the clean and low-carbon transformation of power systems, addressing the challenge of day-ahead electricity market price prediction issues triggered by the strong stochastic volatility of power supply output due to high-penetration renewable energy integration, as well as problems such as limited dataset scales and short market cycles in test sets associated with existing electricity price prediction methods, this paper introduced an innovative prediction approach based on a multi-modal feature fusion and BiGRUSA-ResSE-KAN deep learning model. In the data preprocessing stage, maximum–minimum normalization techniques are employed to process raw electricity price data and exogenous variable data; the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD) methods are utilized for multi-modal decomposition of electricity price data to construct a multi-scale electricity price component matrix; and a sliding window mechanism is applied to segment time-series data, forming a three-dimensional input structure for the model. In the feature extraction and prediction stage, the BiGRUSA-ResSE-KAN multi-branch integrated network leverages the synergistic effects of gated recurrent units combined with residual structures and attention mechanisms to achieve deep feature fusion of multi-source heterogeneous data and model complex nonlinear relationships, while further exploring complex coupling patterns in electricity price fluctuations through the knowledge-adaptive network (KAN) module, ultimately outputting 24 h day-ahead electricity price predictions. Finally, verification experiments conducted using test sets spanning two years from five major electricity markets demonstrate that the introduced method effectively enhances the accuracy of day-ahead electricity price prediction, exhibits good applicability across different national electricity markets, and provides robust support for electricity market decision making.

Research on rolling bearing fault diagnosis method based on AMVMD and convolutional neural networks

A mapping function relation is generated by a variational mode decomposition (VMD) transform, and an adaptive image encryption algorithm based on VMD is proposed. The image sequence is generated using VMD is divided into high frequency, middle frequency, and low frequency according to the entropy value of its mode transformation. The advantages of this algorithm are that the cross-mapping is generated according to VMD, the low-frequency part is the main energy concentration area of the image, the image processing encryption is carried out in the other generated images, the encryption does not affect the original image, and the robustness is improved. The simulation results showed that the algorithm had a good effect of encryption and restoration by measuring the root mean square error and the Euclidean distance. Experiment showed that the proposed method was more robust to the complex distribution of faces than the existing methods considered, yielding favourably comparable results to the state-of-the-art methods on data encryption. The results also showed that the proposed method was scalable in other areas of datasets. Furthermore, we showed that the proposed method did not need the number of features as a prior, was aware of noises and outliers, and could be extended to a multi-view version for more accurate clustering accuracy. These steps, which should require generation of the final output from the styled paper, are mentioned here in this paragraph. First, users have to run Reference Numbering from the Reference Elements menu; this is the first step to start the bibliography marking (it should be clicked while keeping the cursor at the beginning of the reference list). After the marking is complete, the reference element runs all the options under the Cross Linking menu.

Enhancement of adaptive mode decomposition via angular resampling for nonstationary signal analysis of rotating machinery: Principle and applications

Research on Feature Extraction and Separation of Mechanical Multiple Faults Based on Adaptive Variational Mode Decomposition and Comprehensive Impact Coefficient